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1.
Ganesh S. Kadu 《印度理论与应用数学杂志》2011,42(2):73-97
Let (A, m) be a Cohen-Macaulay local ring, M a Cohen-Macaulay A-module of dimension d ≥ 1 and I a proper ideal of analytic deviation one with respect to M. In this paper we study the Cohen-Macaulayness of associated graded module of a Cohen-Macaulay module. We show that if I is generically a complete intersection of analytic deviation one and reduction number at most one with respect to M then G
I
(M) is Cohen-Macaulay. When analytic spread of I with respect to M equals d we prove a similar result when reduction number of an ideal is atmost two. 相似文献
2.
《Quaestiones Mathematicae》2013,36(1):59-66
Abstract In [2], Aupetit studied the perturbation of elements of a Banach algebra A by elements of an inessential ideal I of A. The main result of his paper is based on a lemma ([2], theorem 1.1) obtained by the use of subharmonic methods and analytic multivalued functions. Our aim in this note is to prove Auptetit's perturbation theorem ([2], theorem 2.4) by making use of elementary methods. 相似文献
3.
Idealization of a decomposition theorem 总被引:1,自引:1,他引:0
In 1986, Tong [13] proved that a function f : (X,τ)→(Y,φ) is continuous if and only if it is α-continuous and A-continuous. We extend this decomposition of continuity in terms of ideals. First, we introduce the notions of regular-I-closed sets, A
I-sets and A
I -continuous functions in ideal topological spaces and investigate their properties. Then, we show that a function f : (X,τ,I)→(Y, φ) is continuous if and only if it is α-I-continuous and A
I-continuous.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
4.
Nathalie Gonzalez Sbastien Pellerin Richard Robert 《Journal of Pure and Applied Algebra》2001,160(2-3)
Let A be a UFD and I be an ideal of A. We study the elasticity of atomic domains of the form A+XI[X]. We prove this elasticity to be finite if and only if I is a product of incomparable prime ideals where at most one of them is nonprincipal, then we provide an explicit computation in the finite case. 相似文献
5.
V. S. Luchko 《Ukrainian Mathematical Journal》2009,61(7):1187-1191
Let I be a nilpotent ideal of an associative algebra A over a field F and let D be a derivation of A. We prove that the ideal I + D(I) is nilpotent if char F = 0 or the nilpotency index I is less than char F = p in the case of the positive characteristic of the field F. In particular, the sum N(A) of all nilpotent ideals of the algebra A is a characteristic ideal if char F = 0 or N(A) is a nilpotent ideal of index < p = char F. 相似文献
6.
Erika Giorgi 《代数通讯》2013,41(8):2755-2767
Let A be a commutative Noetherian ring and I an ideal in A. We characterize algebraically when all the minimal primes of the associated graded ring G I A contract to minimal primes of A/I. This, applied to intersection theory, means that there are no embedded distinguished varieties of intersection. The characterization is in terms of the analytic spread of certain localizations of I, the symbolic Rees algebra, and the normalization of the Rees algebra, and extends results of Huneke, Vasconcelos, and Martí-Farré. 相似文献
7.
Natale Paolo Vinai 《manuscripta mathematica》2004,115(3):299-311
We prove that the arithmetic degree of a graded or local ring A is bounded above by the arithmetic degree of any of its associated graded rings with respect to ideal I in A. In particular, if Spec(A) is equidimensional and has an embedded component (i.e., A has an embedded associated prime ideal), then the normal cone of Spec(A) along V(I) has an embedded component too. This extends a result of W. M. Ruppert about embedded components of the tangent cone.Mathematics Subject Classification (2000): Primary 13H15, 13A30; Secondary 13D45, 14Q99 相似文献
8.
Summary We introduce the notion of a semi-I-regular set and investigate some of its properties. We show that it is weaker than the notion of a regular-I-closed set. Additionally, we also introduce the notion of an ABI -set by using the semi-I-regular set and study some of its properties. We conclude that a subset A of an ideal topological space (X,τ,I) is open if and only if it is an ABI -set and a pre-I-open set. 相似文献
9.
We study infinite-dimensional Lie algebras L over an arbitrary field that contain a subalgebra A such that dim(A + [A, L])/A < . We prove that if an algebra L is locally finite, then the subalgebra A is contained in a certain ideal I of the Lie algebra L such that dimI/A <. We show that the condition of local finiteness of L is essential in this statement. 相似文献
10.
In this paper we study the ideal amenability of Banach algebras. LetA be a Banach algebra and letI be a closed two-sided ideal inA, A isI-weakly amenable ifH
1(A,I
*) = {0}. Further,A is ideally amenable ifA isI-weakly amenable for every closed two-sided idealI inA. We know that a continuous homomorphic image of an amenable Banach algebra is again amenable. We show that for ideal amenability
the homomorphism property for suitable direct summands is true similar to weak amenability and we apply this result for ideal
amenability of Banach algebras on locally compact groups. 相似文献
11.
We describe some basic facts about the weak subintegral closure of ideals in both the algebraic and complex-analytic settings. We focus on the analogy between results on the integral closure of ideals and modules and the weak subintegral closure of an ideal. We start by giving a new geometric interpretation of the Reid–Roberts–Singh criterion for when an element is weakly subintegral over a subring. We give new characterizations of the weak subintegral closure of an ideal. We associate with an ideal I of a ring A an ideal I>, which consists of all elements of A such that v(a)>v(I), for all Rees valuations v of I. The ideal I> plays an important role in conditions from stratification theory such as Whitney's condition A and Thom's condition Af and is contained in every reduction of I. We close with a valuative criterion for when an element is in the weak subintegral closure of an ideal. For this, we introduce a new closure operation for a pair of modules, which we call relative weak closure. We illustrate the usefulness of our valuative criterion. 相似文献
12.
We introduce the notions of δ-I- open sets and semi δ-I-continuous functions in ideal topological spaces and investigate some of their properties. Additionally, we obtain decompositions
of semi-I-continuous functions and α-I-continuous functions by using δ-I-open sets.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
13.
We introduce two notions of amenability for a Banach algebra A. LetI be a closed two-sided ideal inA, we sayA is I-weakly amenable if the first cohomology group ofA with coefficients in the dual space I* is zero; i.e.,H
1(A, I*) = {0}, and,A is ideally amenable ifA isI-weakly amenable for every closed two-sided idealI inA. We relate these concepts to weak amenability of Banach algebras. We also show that ideal amenability is different from amenability
and weak amenability. We study theI-weak amenability of a Banach algebraA for some special closed two-sided idealI. 相似文献
14.
Il Yoo 《Applied Mathematics and Optimization》1994,30(3):225-233
In this paper we establish a theorem for the generalized Fresnel class F
A1,A2 ensuring that various functions are in F
A1,A2. We also prove a translation theorem for the analytic Feynman integral of functions in F
A1,A2.This research was supported in part by the Basic Science Research Program, Ministry of Education. 相似文献
15.
Tord Sjödin 《Czechoslovak Mathematical Journal》2007,57(1):67-73
We consider real valued functions f defined on a subinterval I of the positive real axis and prove that if all of f’s quantum differences are nonnegative then f has a power series representation on I. Further, if the quantum differences have fixed sign on I then f is analytic on I. 相似文献
16.
In this paper we investigate the topological localizations of Lie-complete rings. It has been proved that a topological localization of a Lie-complete ring is commutative modulo its topological nilradical. Based on the topological localizations we define a noncommutative affine scheme X = Spf(A) for a Lie-complete ring A. The main result of the paper asserts that the topological localization A(f) of A at f ∈ A is embedded into the ring 𝒪A(Xf) of all sections of the structure sheaf 𝒪A on the principal open set Xf as a dense subring with respect to the weak I1-adic topology, where I1 is the two-sided ideal generated by all commutators in A. The equality A(f) = 𝒪A(Xf) can only be achieved in the case of an NC-complete ring A. 相似文献
17.
In this paper we investigate and compare the properties of the semigroup generated by A, and the sequence
where Ad = (I + A) (I − A)−1.
We show that if A and A−1 generate a uniformly bounded, strongly continuous semigroup on a Hilbert space, then Ad is power bounded. For analytic semigroups we can prove stronger results. If A is the infinitesimal generator of an analytic semigroup, then power boundedness of Ad is equivalent to the uniform boundedness of the semigroup generated by A. 相似文献
18.
Michael Peretzian Williams 《代数通讯》2013,41(6):1843-1849
We find examples of nilpotent n-Lie algebras and prove n-Lie analogs of classical group theory and Lie algebra results. As an example we show that a nilpotent ideal I of class c in a n-Lie algebra A with A/I 2 nilpotent of class d is nilpotent and find a bound on the class of A. We also find that some classical group theory and Lie algebra results do not hold in n-Lie algebras. In particular, non-nilpotent n-Lie algebras can admit a regular automorphism of order p, and the sum of nilpotent ideals need not be nilpotent. 相似文献
19.
Sérgio Alvarez Lev Birbrair João Carlos Ferreira Costa Alexandre Fernandes 《Central European Journal of Mathematics》2010,8(2):338-345
We study the topological K-equivalence of function-germs (ℝ
n
, 0) → (ℝ, 0). We present some special classes of piece-wise linear functions and prove that they are normal forms for equivalence
classes with respect to topological K-equivalence for definable functions-germs. For the case n = 2 we present polynomial models for analytic function-germs. 相似文献
20.
Daniele Mundici 《Milan Journal of Mathematics》2011,79(2):643-656
In a recent paper, F. Boca investigates the AF algebra
\mathfrakA{{\mathfrak{A}}} associated with the Farey-Stern-Brocot sequence. We show that
\mathfrakA{{\mathfrak{A}}} coincides with the AF algebra
\mathfrakM1{{\mathfrak{M_{1}}}} introduced by the present author in 1988. As proved in that paper (Adv. Math., vol.68.1), the K
0-group of
\mathfrakA{\mathfrak{A}} is the lattice-ordered abelian group M1{\mathcal{M}_{1}} of piecewise linear functions on the unit interval, each piece having integer coefficients, with the constant 1 as the distinguished
order unit. Using the elementary properties of M1{\mathcal{M}_{1}} we can give short proofs of several results in Boca’s paper. We also prove many new results: among others,
\mathfrakA{{\mathfrak{A}}} is a *-subalgebra of Glimm universal algebra, tracial states of
\mathfrakA{{\mathfrak{A}}} are in one-one correspondence with Borel probability measures on the unit real interval, all primitive ideals of
\mathfrakA{{\mathfrak{A}}} are essential. We describe the automorphism group of
\mathfrakA{{\mathfrak{A}}} . For every primitive ideal I of
\mathfrakA{{{\mathfrak{A}}}} we compute K
0(I) and
K0(\mathfrakA/I){{K_{0}(\mathfrak{A}/I)}}. 相似文献